This is a completely free tool.
It is hard to get rid of all bugs, and I cannot make guarantee for the functionality of the tool. If you find any bug when using it, please contact with me. I promise that most of the problems (expect those caused only by your computer) could be solved in time.
3. 本工具基于Matlab 2015a GUI开发，因此，你的电脑中可能需要安装Matlab Runtime 2015a，具体请看此页。
This tool is developed based on Matlab 2015a GUI, thus you might need to install Matlab Runtime 2015a in advance. You can refer to this page.
功能介绍 Introduction of Functionality
The so-called commute pattern refers to the trip distribution matrix among zones. The main function of this tool is to calculate different kinds of trip distribution matrices given traffic cost and total population & jobs of zones. In fact, non-commuting trip patterns could also be analyzed in the similar way.
一方面，用户可以利用经典的重力模型求得基于重力模型的通勤交通分布矩阵。这里的重力模型不同于城市地理学常用的哈夫（Huff）模型。哈夫模型是单约束重力模型，只保证从每个小区出发的总出行量等于该小区的总人口数，而不能保证到达每个小区的总交通量等于该小区的总就业数，该模型相对简单，ArcGIS已经提供了工具。本工具采用的重力模型是双约束重力模型，在总人口与总就业上都保证约束条件的成立。重力模型中的阻抗函数采用倒幂函数f(cost) = cost-b，其中的b被称为扩散参数，需要指定。如果用户能够提供一个观察到的实际交通分布矩阵，那么本工具可以完成对b的估计。
First, users could employ classical gravity model to generate a commute-trip distribution matrix. The gravity model of this tool is different from Huff model, which is commonly used in urban geography. Huff model is a singly-constrained gravity model: the sum of trips leaving from a zone equals the total population of that zone, while the sum of trips arriving at a zone does not necessarily equals the total jobs of that zone. Huff model is relatively simple, and already available in ArcGIS. On the other side, the gravity model in this tool is a doubly-constrained one, which make constraints on both total population and jobs. The impedance function of the gravity model is the inverse function f(cost) = cost-b，where b is commonly referred as dispersion parameter, which needs to be set. If users could import an observed trip distribution matrix, this tool could help to estimate the value of b.
Users could also adopt linear program method to generate a theoretically optimal commute-trip distribution matrix, which minimizes the average traffic cost of all commuters.
The trip distribution based on gravity matrix could be viewed as expected result with practical meanings, while the optimal trip distribution is an ideal situation. This tool would calculate average traffic cost of all commuters of different trip distribution patterns, and if the users provide observed trip distribution matrix, they are able to make comparisons among average traffic costs of different commute patterns, and evaluate possible redundant commutes.
视频示例 Video Demo
Supposing the traffic cost between zone i and zone j is dij, the total population of zone i is Pi, the total jobs of zone j is Aj, and the dispersion parameter is b.
Supposing the number of commuters from zone i to zone j is Tij, the average traffic cost of all commuters (c) could be easily calculated as follows.
c = ∑i∑jTijdij / ∑i∑jTij
According to doubly-constrained gravity model, the count of commuters Tij from zone i to zone j could be calculated as follows.
Tij = ai * Pi * bj * Aj * f(dij)
∑jTij = Pi , ∑iTij = Aj
f(dij) = (dij)-b (b>0)
ai and bj are balance coefficients of row i and column j respectively. Since they are mutually dependent on each other, it is difficult to directly solve them, and an iterative method would be applied as follows.
ai = 1 / ∑kbkAkf(dik)
bj = 1 / ∑kakPkf(dkj)
When calibrating parameter b of gravity model using observed commute trip distribution, the classical way is to minimize difference between gravity-model-predicted average traffic cost and observed average traffic cost. Following iterative method could be applied to solve this problem, where c* refers to observed average traffic cost, c(k) refers to gravity-model-predicted average traffic cost at iteration k, and b(k) refers to the value of b at iteration k.
Iteration 1: b(1) = 1 / c*
Iteration 2: b(2) = b(1)c(1) / c*
Iteration 3 and afterwards: b(k) = ((c(k-1) – c*)b(k-2) – (c(k-2) – c*)b(k-1)) / (c(k-1) – c(k-2))
In addition to this classical method, this tool also provides genetic algorithm (GA) option. GA could either set the closest average traffic cost as the object, or attempt to generate a closest predicted commute trip matrix as the observed matrix. Please note that GA would generally require more solving time.
As to optimal trip distribution problem, a linear program model is employed, as follows.
min: c = ∑i∑jTijdij / ∑i∑jTij
Subject to: ∑jTij = Pi , ∑iTij = Aj